The following line passes through point $(4, 7)$ : $y = \dfrac{12}{5} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(4, 7)$ into the equation gives: $7 = \dfrac{12}{5} \cdot 4 + b$ $7 = \dfrac{48}{5} + b$ $b = 7 - \dfrac{48}{5}$ $b = -\dfrac{13}{5}$ Plugging in $-\dfrac{13}{5}$ for $b$, we get $y = \dfrac{12}{5} x - \dfrac{13}{5}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(4, 7)$